Among additive processes we frequently focus on
Lévy processes which additionally have stationary increments property, so that the
system of generating triplet of \(V\)  is given by \(\lbrace u (A,\rho ,\gamma ):u\ge 0\rbrace \)  (see [1]}). Particularly we are interested
in the class of subordinators (cf. [1]}) of
which Laplace transform (LP for short) is
\({\mathbb {E}}[e^{-xV(1)}] = \exp \big \lbrace -\gamma x + \int _{(0,\infty )}(e^{-xv}-1)\nu (dv)\big \rbrace ,\quad x\ge 0\) 
